4t^2+5-60=0

Solution for 4t^2+5-60=0 equation:

4t^2+5-60=0

We add all the numbers together, and all the variables

4t^2-55=0

a = 4; b = 0; c = -55;
Δ = b2-4ac
Δ = 02-4·4·(-55)
Δ = 880
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{55}}{2*4}=\frac{0-4\sqrt{55}}{8}
=-\frac{4\sqrt{55}}{8}
=-\frac{\sqrt{55}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{55}}{2*4}=\frac{0+4\sqrt{55}}{8}
=\frac{4\sqrt{55}}{8}
=\frac{\sqrt{55}}{2}
$